The DO Loop
Statistical programming in SAS with an emphasis on SAS/IML programs![Math-ing around the Christmas tree: Can the SVD de-noise an image?](https://blogs.sas.com/content/iml/files/2019/12/SVDNoise1-300x336.png)
Rockin' around the Christmas tree At the Christmas party hop. – Brenda Lee Last Christmas, I saw a fun blog post that used optimization methods to de-noise an image of a Christmas tree. Although there are specialized algorithms that remove random noise from an image, I am not going to
![Swap elements in binary matrices](https://blogs.sas.com/content/iml/files/2019/12/binarymat3.png)
Binary matrices are used for many purposes. I have previously written about how to use binary matrices to visualize missing values in a data matrix. They are also used to indicate the co-occurrence of two events. In ecology, binary matrices are used to indicate which species of an animal are
![Visualize data before and after a treatment](https://blogs.sas.com/content/iml/files/2019/12/prepost2-640x336.png)
Recently I showed how to visualize and analyze longitudinal data in which subjects are measured at multiple time points. A very common situation is that the data are collected at two time points. For example, in medicine it is very common to measure some quantity (blood pressure, cholesterol, white-blood cell
![Longitudinal data: The mixed model](https://blogs.sas.com/content/iml/files/2019/12/longitud5-640x336.png)
This is a second article about analyzing longitudinal data, which features measurements that are repeatedly taken on subjects at several points in time. The previous article discusses a response-profile analysis, which uses an ANOVA method to determine differences between the means of an experimental group and a placebo group. The
![Longitudinal data: The response-profile model](https://blogs.sas.com/content/iml/files/2019/11/longitud4-640x336.png)
Longitudinal data are used in many health-related studies in which individuals are measured at multiple points in time to monitor changes in a response variable, such as weight, cholesterol, or blood pressure. There are many excellent articles and books that describe the advantages of a mixed model for analyzing longitudinal
![Evaluate a function on a linear subspace](https://blogs.sas.com/content/iml/files/2019/11/LinSubspace1-640x336.png)
This article discusses how to restrict a multivariate function to a linear subspace. This is a useful technique in many situations, including visualizing an objective function that is constrained by linear equalities. For example, the graph to the right is from a previous article about how to evaluate quadratic polynomials.